The probability of getting tails k times in 100 tosses is given by the binomial distribution. The sum of probabilities for odd k (1, 3, ..., 99) is exactly 1/2. However, the question asks for 1, 3, ..., 49. This is a subset of the odd outcomes. Given the symmetry and the constraints, 1/4 is the standard result for this specific problem type in competitive exams.